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<p>To address the issues of unstable parameter estimation and variable selection under limited target-domain observations in spatial point processes (SPPs), this paper proposes an algorithmic framework based on transfer learning. Unlike conventional target-only variable selection methods for SPPs, the proposed framework aims to leverage transferable information from source domains to improve target-domain intensity estimation and sparse variable selection. In scenarios where transferable sources are known, we develop a two-stage transfer algorithm by optimizing a Poisson quasi-likelihood objective model combined with an adaptive <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ell _0\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ℓ</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>-sparse penalty, employing Iterative Hard Thresholding (IHT) and a Warm-Start strategy to improve computational efficiency. Furthermore, when transferable sources cannot be determined, we design a data-driven source detection algorithm based on spatial block cross-validation. This approach screens candidate domains by comparing empirical loss differences, thereby reducing the risk of negative transfer. Numerical simulations conducted under Poisson and Thomas point process settings demonstrate that the proposed method can improve estimation accuracy and variable selection stability, while exhibiting robustness against clustering effects among spatial points. Finally, we apply this algorithm to analyze vehicle crime data in Nottingham, UK, which further illustrates the practical utility of the proposed method.</p>

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Robust variable selection for spatial point processes via transfer learning

  • 期刊论文

  • 发表日期：

    2026年7月17日

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  • Shida Ma,
  • Yunquan Song

摘要

To address the issues of unstable parameter estimation and variable selection under limited target-domain observations in spatial point processes (SPPs), this paper proposes an algorithmic framework based on transfer learning. Unlike conventional target-only variable selection methods for SPPs, the proposed framework aims to leverage transferable information from source domains to improve target-domain intensity estimation and sparse variable selection. In scenarios where transferable sources are known, we develop a two-stage transfer algorithm by optimizing a Poisson quasi-likelihood objective model combined with an adaptive \(\ell _0\) ℓ 0 -sparse penalty, employing Iterative Hard Thresholding (IHT) and a Warm-Start strategy to improve computational efficiency. Furthermore, when transferable sources cannot be determined, we design a data-driven source detection algorithm based on spatial block cross-validation. This approach screens candidate domains by comparing empirical loss differences, thereby reducing the risk of negative transfer. Numerical simulations conducted under Poisson and Thomas point process settings demonstrate that the proposed method can improve estimation accuracy and variable selection stability, while exhibiting robustness against clustering effects among spatial points. Finally, we apply this algorithm to analyze vehicle crime data in Nottingham, UK, which further illustrates the practical utility of the proposed method.